HDFC lends 1 million to HUDCO at `10%` simple interest p.a. for 2 years and HUDCO lends the same amount to SAHARA STATES HOUSING corporation at `10%` p.a. of compound interest for 2 years What is the earning, of HUDCO in this way ?

Options

A. `₹ 10000`
B. `₹ 33100`
C. `₹ 131000`
D. no profit no loss

Answer

To solve the problem, we need to calculate the interest earned by HUDCO from both HDFC and SAHARA STATES HOUSING corporation.

### Step 1: Calculate the interest earned by HUDCO from HDFC
HDFC lends 1 million at a simple interest rate of 10% per annum for 2 years.

**Formula for Simple Interest (SI):**
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (1 million)
- \( R \) = Rate of interest (10%)
- \( T \) = Time period in years (2 years)

**Calculation:**
\[ \text{SI} = \frac{1,000,000 \times 10 \times 2}{100} \]
\[ \text{SI} = \frac{1,000,000 \times 20}{100} \]
\[ \text{SI} = \frac{20,000,000}{100} \]
\[ \text{SI} = 200,000 \]

So, the interest earned by HUDCO from HDFC is **200,000**.

### Step 2: Calculate the amount received by HUDCO from SAHARA STATES HOUSING corporation
HUDCO lends the same amount (1 million) to SAHARA STATES HOUSING corporation at a compound interest rate of 10% per annum for 2 years.

**Formula for Compound Interest (CI):**
\[ \text{A} = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount (1 million)
- \( R \) = Rate of interest (10%)
- \( T \) = Time period in years (2 years)

**Calculation:**
\[ A = 1,000,000 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 1,000,000 \left(1 + 0.1\right)^2 \]
\[ A = 1,000,000 \left(1.1\right)^2 \]
\[ A = 1,000,000 \times 1.21 \]
\[ A = 1,210,000 \]

### Step 3: Calculate the interest earned by HUDCO from SAHARA STATES HOUSING corporation
The interest earned from SAHARA STATES HOUSING corporation is the total amount received minus the principal.

**Calculation:**
\[ \text{Interest} = A - P \]
\[ \text{Interest} = 1,210,000 - 1,000,000 \]
\[ \text{Interest} = 210,000 \]

So, the interest earned by HUDCO from SAHARA STATES HOUSING corporation is **210,000**.

### Step 4: Calculate the total earning of HUDCO
Now, we can find the total earning of HUDCO by subtracting the interest paid to HDFC from the interest earned from SAHARA STATES HOUSING corporation.

**Calculation:**
\[ \text{Total Earning} = \text{Interest from SAHARA} - \text{Interest paid to HDFC} \]
\[ \text{Total Earning} = 210,000 - 200,000 \]
\[ \text{Total Earning} = 10,000 \]

Thus, the total earning of HUDCO in this way is **10,000**.